Definition: All parts of an object are affected by gravity. From the effect point of view, we can think that the gravity of each part is concentrated on one point, which is called the center of gravity of the object.
The position of the center of gravity of an object is an object with uniform mass distribution (uniform object), and the position of the center of gravity is only related to the shape of the object. For objects with regular shapes, the center of gravity is on the geometric center of gravity. For example, the center of a uniform thin straight rod is at the midpoint of the rod, the center of gravity of a uniform sphere is at the center of the sphere, and the center of gravity of a uniform cylinder is at the midpoint of the shaft. The center of gravity of irregular objects can be determined by hanging method.
For objects with uneven mass distribution, the position of the center of gravity is not only related to the shape of the object, but also related to the mass distribution inside the object. The center of gravity of the truck changes with the change of loading capacity and loading position, and the center of gravity of the crane changes with the weight and height of the hoisted object.
An object or figure is divided into two parts by the straight line or tangent plane of the center of gravity, so the volumes or areas of the two parts are not necessarily equal. Not all straight lines or tangent planes passing through the center of gravity bisect the area or volume of an object or figure. For example, a straight line passing through the center of gravity of a regular triangle and parallel to one side divides the triangle into two parts with an area ratio of 4: 5. This can be explained by the lever principle of physics: the distance from the center of gravity of two divided figures to the center of gravity of a triangle is equivalent to the two arms of the lever, and the area of the two figures is equivalent to the two forces of the lever. Because the center of gravity is equivalent to the point where two graphic areas are "concentrated" (refer to the definition of the center of gravity). Like the above example, the distance between the center of gravity of the two divided figures and the center of gravity of the triangle is exactly equal to 5: 4. If you are interested, you can prove it by drawing with geometric sketchpad software.
I have made it very clear, mainly in physics, of course, it is also called the center of gravity in mathematics, but we all think that the density of the figures studied in mathematics is equal. As the name implies, the center of gravity is the center of weight. Because the density is equal, the areas of the two parts must be equal. Of course, this is only for quadrangles, but the areas of triangles are not equal. The center of gravity in mathematical geometry is only a special case of the center of gravity in physics.